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"... This paper studies the notions of approximation and passage to the limit in an axiomatic setting. Our axiomatisation is subject to the following criteria: the axioms should be natural (so that they are available in as many contexts as possible) and non-order-theoretic (so that Research supported b ..."

This paper studies the notions of approximation and passage to the limit in an axiomatic setting. Our axiomatisation is subject to the following criteria: the axioms should be natural (so that they are available in as many contexts as possible) and non-order-theoretic (so that Research supported by SERC grant RR30735 and EC project Programming Language Semantics and Program Logics grant SC1000 795 they explain the order-theoretic structure). Our aim is 1. to provide a justification of Scott&apos;s original consideration of ordered structures, and 2. to deepen our understanding of the notion of passage to the limit